<h2>Problem 148</h2>
<div style="color:#666;font-size:80%;">07 April 2007</div><br />
<div class="problem_content">
<p>We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by 7:</p>
<table cellpadding='0' cellspacing='0' border='0' align='center'>
<tr>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
</tr>
<tr>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
</tr>
<tr>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
<td>&nbsp;</td>
<td>&nbsp;2</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
</tr>
<tr>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
<td>&nbsp;</td>
<td>&nbsp;3</td>
<td>&nbsp;</td>
<td>&nbsp;3</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
</tr>
<tr>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
<td>&nbsp;</td>
<td>&nbsp;4</td>
<td>&nbsp;</td>
<td>&nbsp;6</td>
<td>&nbsp;</td>
<td>&nbsp;4</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
</tr>
<tr>
<td>&nbsp;</td>
<td>&nbsp;1</td>
<td>&nbsp;</td>
<td>&nbsp;5</td>
<td>&nbsp;</td>
<td>10</td>
<td>&nbsp;</td>
<td>10</td>
<td>&nbsp;</td>
<td>&nbsp;5</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
</tr>
<tr>
<td>1</td>
<td>&nbsp;</td>
<td>&nbsp;6</td>
<td>&nbsp;</td>
<td>15</td>
<td>&nbsp;</td>
<td>20</td>
<td>&nbsp;</td>
<td>15</td>
<td>&nbsp;</td>
<td>&nbsp;6</td>
<td>&nbsp;</td>
<td>&nbsp;1</td>
</tr>
</table>
<p>However, if we check the first one hundred rows, we will find that only 2361 of the 5050 entries are <i>not</i> divisible by 7.</p>

<p>Find the number of entries which are <i>not</i> divisible by 7 in the first one billion (10<img src="" style="display:none;" alt="^(" /><sup>9</sup><img src="" style="display:none;" alt=")" />) rows of Pascal's triangle.</p>
</div><br />
